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Does America have too many immigrants? That is a question which sparks heated political debate in Washington. Little wonder. Earlier this year Barack Obama pledged to make immigration reform a central plank of his second term as president.

But while that won him support among Hispanic voters, it infuriated many Republicans, particularly in the South. And with the unemployment rate remaining stubbornly high, the issue is doubly controversial due to a perception – or fear – that immigrants are stealing American jobs.

Last week a curious new salvo was fired into this fiery debate from none other than the Dallas Federal Reserve. In recent years, this institution has earned a reputation for being one of the more independent-minded parts of the Fed: its president, Richard Fisher, has demanded policies to slash the size of banks, and its officials take a free-market, conservative view. (Indeed, as a sign of this Wild West heritage, it is the only western central bank I have ever seen where an official notice tells customers to put their guns aside before entering.)

But when it comes to immigration – of the legal and illegal kind – the Lone Star Fed is not sitting with the Tea Party core. On the contrary, it has just published a paper – under the provocative title “Gone to Texas” – arguing that immigration is good for the local economy. And it rebuffs the idea that immigrants are stealing jobs from native-born Americans. On the contrary, it insists, they tend to boost growth in a win-win way.

Now, if this conclusion had emerged in a state with few immigrants and plenty of unfilled jobs (think North Dakota), that might be unsurprising. But the picture that Fed researchers paint of Texas is eye-popping. Since 1990, the number of foreign-born people living there has jumped from 1.5 million to 4.3 million, they say, noting that “Texas [now] has more immigrants than Oklahoma and New Mexico have people”, and that “among large states, none has experienced a surge like Texas has, with immigrants rising from 9 per cent of the population in 1990 to 16.4 per cent in 2012”.

Some immigrants are highly skilled, lured by the fast-growing energy sector, for example. But most are not: two-thirds do not have a high-school diploma, two-thirds come from Mexico, and almost half – or 1.8 million people – are illegal, according to the Fed’s number crunchers. If you want to find a poster child for the vision of Mexicans flooding illegally across the border to work in American fields and factories, Texas is perfect.

But that has not hurt native-born Americans, the Fed insists. “When immigrants flow into the labour force, it is not just a matter of adding more workers. As long as immigrants differ from natives – which they do to varying degrees – specialisation occurs,” the report observes. Furthermore, “Less-educated US natives have a comparative advantage in communications-intensive jobs, and less-educated immigrants in manual-labour jobs.” Or to put it another way, Mexican tomato pickers do not compete with American receptionists (not least because almost half of the immigrants in the study apparently have few or no English-language skills).

What immigration does do is lower the price of “immigrant-produced goods and services”, which equates to an income gain of $3.4bn-$6.6bn a year, the study suggests. And while this needs to be offset against the rising strain on public infrastructure and services, this is not such a big issue in bare-bones Texas, which has “a skimpy safety net and lower levels of publicly provided services than other large states”.

I daresay such conclusions will horrify many observers on both sides of the political divide. To Tea Party supporters, it seems hard to believe that illegal immigrants do not displace American jobs; to leftwing economists, it seems even more abhorrent to think that businesses could be booming on the back of unprotected cheap labour. In any case, as both left and rightwing economists might point out, Texas is something of an exceptional case: its economy has been unusually fast growing in recent years, partly because of the energy boom, which has created plenty of new jobs – for immigrants and non-immigrants alike.

When it comes to immigration, the state is also unusual in political terms in that the influx of newcomers has occurred under governors of both the Democrat (Ann Richards) and Republican persuasions (George W Bush and Rick Perry). As president, Bush was also a strong advocate for immigration reform.

If nothing else, the results of the study are intriguing, particularly given that immigration reform will almost certainly rear its head in Congress soon, as Obama tries to define his legacy. The only pity is that the Dallas Fed paper did not look at another curious and counter-intuitive recent development: namely, that in the past year it seems that the flow of those unskilled Mexicans north has slowed, if not stalled. And if that continues, it could twist the immigration debate yet again – not just in the Lone Star state but in Washington too.